need help with this please 7 Prob #2-64 Question 8 (of 18) value: 2.00 points Am

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need help with this please

7 Prob #2-64 Question 8 (of 18) value: 2.00 points Among U.S. cities with a population of more than 250,000, the mean one-way commute time to work is 24.3 minutes. The longest one-way travel time is in New York City, where the mean time is 38.3 minutes. Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.5 minutes. a. What percent of the New York City commutes are for less than 30 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.) Percent 0.1342 % b. What percent are between 30 and 35 minutes? (Round the intermediate values to 2 decimal places Round your answer to 2 decimal places.) . Percent 0.1958 % c. What percent are between 30 and 40 minutes? (Round the intermediate values to 2 decimal places. Round your answer to 2 decimal places.) Percent 0.4555 % References eBook & Resources Worksheet Difficulty: 2 Intermediate Learning Objectiv calculate probabili O Type here to search 21

Explanation / Answer

Solution(a)
Given in the question
mean = 38.3 and Standard deviation = 7.5
P(Xbar<30)

Z = (30-38.3)/7.5 = -1.10666
from the z table we found that
P(Xbar<30) = 0.1335 or 13.35%

Solution(b)
P(30<Xbar<35) = P(Xbar<35) - P(Xbar<30)
Z = (35-38.3)/7.5 = -3.3/7.5 = -0.44
P(30<Xbar<35) = 0.33-0.1335 = 0.1965 or 19.65%
Solution(C)
P(30<Xbar<40)=P(Xbar<40)-P(Xbar<30)
Z = (40-38.3)/7.5 = 1.7/7.5 = 0.22666
P(30<xbar<40) = 0.5910-0.1335 = 0.4575 or 45.75%

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